Exercise Identify the premises and conclusion of each argument. Some of these can be done in more than one way. 1. John has brown hair. John is not blond. 2. Mary had a little lamb. Mary had five lambs. 3. I still have five tin cans. I received three cans when I was younger. I received two cans when I was older. I did not throw any cans away. 4. Mary is shorter than John. John is the tallest person in the world. 5. Susan is taller than John. Susan is taller than Mary. John is taller than Mary. 6. John likes broccoli or cabbage, but not both. John does not like broccoli. John likes cabbage. 7. Mary is not at home. If she were home, she would answer her door. She isn't answering her door. 8. My dog is better than your cat. Any dog is better than any cat. 9. All the ravens I’ve seen so far are black. All ravens are black.
Deductive and Inductive There are two ways in which the premises of an argument might support the conclusion. Inductively: The premises provide reliable evidence for the likelihood of the conclusion. Example: 1. The postman has always come by at 2pm before. 2. The postman will come by at 2pm today. Deductively: The premises guarantee the truth of the conclusion. Example: 1. Judy either is at the store or at home. 2. Judy isn’t at home. 3. Judy is at the store.
Exercise State whether each of the following arguments is deductive or inductive. 1. The plaque on the leaning tower of Pisa says that Galileo performed experiments there. 2. Galileo did indeed perform experiments there. 1. There were pry marks around the lock on the rear door. 2. There were deposits of mud near the rear threshold. 3. The burglar entered through the rear door. 1. Either global warming will be arrested, or hurricanes will become more intense. 2. Global warming will not be arrested. 3. Hurricanes will become more intense.
Validity Deductive arguments are valid in the following sense. – An argument is invalid = there is a conceivable scenario in which the premises are true and the conclusion is false. – If an argument is not invalid, then it is valid.
Valid and Invalid Arguments Examples: 1. If Socrates was a philosopher, then he wasn’t a historian. 2. Socrates wasn’t a historian. 3. Socrates was a philosopher. 1. All men are mortal. 2. Socrates is a man. 3. Socrates is mortal. 1. If Col. Mustard is the murderer, then the murder weapon is the wrench. 2. The murder weapon is not the wrench. 3. Col. Mustard is not the murderer. 1. Every plant has nine toes. 2. President Obama is a plant. 3. President Obama has nine toes.
Soundness As the Obama-is-a-plant example shows, an argument can be valid without being successful. In order to be successful, an argument must be sound. – And argument is sound = its premises are true and it is valid.
Exercise State whether each of the following arguments is or isn’t valid and/or sound. 1. If she studies hard, she will do well. She studied hard. Therefore she will do well. 2. If I leave home early enough, I will get to school on time. I got to school on time. Therefore, I must have left home early enough. 3. People that smoke raise their chances of getting cancer. Alice died from cancer. She must have been smoking too much. 4. Bob has five kids. So, he has three kids. 5. All dogs are cats. All cats are terrible. Therefore, all dogs are terrible. 6. Mammals nurse their young with milk. Tigers are mammals. So, tigers nurse their young with milk.
Exercise 3 1. Come up with 2 valid arguments. 2. Come up with 2 invalid arguments. 3. Come up with 2 sound arguments. 4. come up with 2 unsound arguments. Answers to 3 and 4 should be different from answers to 1 and 2.